Abstract

This paper presents the \(\mathcal {S}\)-procedure characterization for the stabilization of positive switched linear systems and establishes the relationship between the \(\mathcal {S}\)-procedure and its equivalent Lyapunov–Metzler inequalities. First, a piecewise linear co-positive Lyapunov function is constructed for positive switched linear systems. Under the Lyapunov function, the \(\mathcal {S}\)-procedure stabilization for positive switched linear systems in the continuous-time context is explored under a min state switching law. The \(\mathcal {S}\)-procedure conditions are formulated in the form of linear programming. Finally, an equivalence relationship between \(\mathcal {S}\)-procedure and Lyapunov–Metzler inequalities is presented.

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